Hölder regularity for hypoelliptic kinetic equations with rough diffusion coefficients

Abstract

This paper is dedicated to the application of the DeGiorgi-Nash-Moser regularity theory to the kinetic Fokker-Planck equation. This equation is hypoelliptic. It is parabolic only in the velocity variable, while the Liouville transport operator has a mixing effect in the position/velocity phase space. The mixing effect is incorporated in the classical DeGiorgi method via the averaging lemmas. The result can be seen as a Hölder regularity version of the classical averaging lemmas.

21 pages. Statement of Lemma 3.2 corrected. Proof of Lemma 3.2 modified accordingly